{
  "id": "2203.11371",
  "version": "v1",
  "published": "2022-03-21T22:15:48.000Z",
  "updated": "2022-03-21T22:15:48.000Z",
  "title": "Soliton dynamics for the 1D quadratic Klein-Gordon equation with symmetry",
  "authors": [
    "Yongming Li",
    "Jonas Luhrmann"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish the conditional asymptotic stability in a local energy norm of the unstable soliton for the one-dimensional quadratic Klein-Gordon equation under even perturbations. A key feature of the problem is the positive gap eigenvalue exhibited by the linearized operator around the soliton. Our proof is based on several virial-type estimates, combining techniques from the series of works [23-26, 28], and an explicitly verified Fermi Golden Rule. The approach hinges on the fact that even perturbations are orthogonal to the odd threshold resonance of the linearized operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-21T22:15:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "1d quadratic klein-gordon equation",
      "soliton dynamics",
      "verified fermi golden rule",
      "one-dimensional quadratic klein-gordon equation",
      "conditional asymptotic stability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}